Notes on overt choice - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Computability Year : 2023

Notes on overt choice

Abstract

Overt choice was recently introduced and thoroughly studied by de Brecht, Pauly and Schröder. They give estimates on the Weihrauch degree of overt choice on various spaces, and relate it to the topological properties of the space. In this article, we pursue this line of research, answering some of the questions that were left open. We show that overt choice on the rationals is not limit-computable. We identify the Weihrauch degree of overt choice on the space of natural numbers with the co-finite topology. We prove that the quasi-Polish spaces are the countably-based T0-spaces on which a variant of overt choice, called Π 0 2 overt choice, is continuous. It extends a previous result that holds in the class of T1-spaces. We also prove an effective version of this equivalence.
Fichier principal
Vignette du fichier
article (1).pdf (385.41 Ko) Télécharger le fichier
article.pdf (388.71 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

hal-04164138 , version 1 (18-07-2023)
hal-04164138 , version 2 (06-09-2023)

Licence

Attribution

Identifiers

Cite

Mathieu Hoyrup. Notes on overt choice. Computability, 2023, pp.1-19. ⟨10.3233/COM-230458⟩. ⟨hal-04164138v2⟩
28 View
20 Download

Altmetric

Share

Gmail Facebook X LinkedIn More